And yet using it to play Skyrim on medium preset ends up with massive lagging to the point of becoming unplayable. Low preset does fine, but I'd like to experience better graphics.
Here is the page for the system requirements of Skyrim:
<!-- m --><a class="postlink" href="http://www.uesp.net/wiki/Skyrim:System_Requirements">http://www.uesp.net/wiki/Skyrim:System_Requirements</a><!-- m -->

Sorry for bothering, but I'm going to buy a new desktop soon, and I want to get it right without having my money going down the drain.

Here is the thing.... your brother's laptop also appears to have NVIDIA Optimus installed. Basically, this means that his laptop has both the 525m and an integrated Intel GPU. Optimus works by having some programs and games run their graphics power through the 525m rather than the integrated Intel graphics so you can get better performance, and also better battery life since the 525m isn't in constant use. In short, Optimus is behind-the-scenes GPU switching.

One theory as to why you can't play Skyrim on medium settings is that the game is using the integrated Intel GPU instead of the 525M. To check, follow these instructions...

1: Right click on the desktop, and select "NVIDIA Control Panel".

2: In the window that appears, look to the left and expand the "3D Settings" tree, if it's not expanded already.

3: Click on "Manage 3D Settings"

4: To the right, the Manage 3D Settings option will appear. Click on the "Program Settings" tab.

5: Under "Program Settings" is a drop down box of programs that the NVIDIA drivers have detected. Open that list and see if Skyrim is on the list. If it's on the list, select "Skyrim" and look below for another drop down box, which determines which GPU to use. If this box says "High Performance NVIDIA processor", nothing else needs to be done. If this box says "Integrated Graphics" however, change it to "High Performance NVIDIA processor" and click on "Apply".

6: However, if Skyrim is not on the programs list, you need to click on the "Add" button next to the program drop down box and navigate to the directory where the Skyrim .EXE is located. Click on that, and Skyrim should be added to the list.

If Skyrim is indeed using the NVIDIA GPU and it's not running at Medium settings, you need to try and check the NVIDIA control panel settings for that particular program.

If not, then you probably need to play Skyrim on a computer that has a better graphics processor.